Question

The decimal expansion of the rational number
2137/1050
(a) terminating
(b) non-terminating repeating.
(c) non-terminating non-repeating. (d) none of these.​

Answer 1

Answer:

Non terminating repeating (b)

Step-by-step explanation:

It won't be (c) as only irrational numbers which can't be expressed as fractions have non terminating non repeating decimal expansions.

So we have (a) and (b).

When we express the denominator as a product of primes, we get,

1050= 2×5×5×3×7

Since the denominator does not have only 2 and 5 as factors, it will not have a terminating decimal expansion.

We must know that any fraction with terminating decimal expansion has only 2 or 5 or both as the factors of its denominator.

I do hope it was helpful and informative.